Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.astro.spbu.ru/staff/afk/AtDatCentre/AtDatCat/Chapter3.pdf Дата изменения: Fri Nov 19 16:06:59 2010 Дата индексирования: Tue Oct 2 04:13:06 2012 Кодировка: Поисковые слова: http astrokuban.info astrokuban

Chapter 3 Collision processes 3.1 Electron impact ionization Collisions of atoms and ions with electrons, protons and other particles can also have effect up on the gas ionization degree in nebulae. The collisional ionization rate increases rapidly at higher values of gas temp erature. In planetary nebulae the most effective are the electron impacts in which an essential fraction of kinetic energy will b e wasted for the atom ionization: Xi (nl)+ e Xi+1 ()+ e + e , where e and e are the electron states b efore and after the ionizing collision with ions Xi . Here e is the removal electron, is the quantum numb er set of the atomic remnant and nl is the same for removal electron. For nebulae the rate of collisional ionization in atom impacts with heavy particles is relatively small and can b e neglected. The numb er of collisional ionization acts resulting from the ion Xi impacts with electrons p er unit volume and unit time is given by N = n(Xi ) ne q1c (Te ) , where q1c = v
1c

is the collisional ionization rate. The ionization cross-section

1c

and, conse-

quently, the ionization rate for different atoms have b een determined by numerous authors. Most often are used the approximation expressions for q
1c

found by Lotz (1967, 1968) for atoms from

H to Ca. Shull & Van Steenb erg (1982) using the exp erimental and theoretical cross-sections of collisional ionization have found simple approximation formula for collisional ionization of all ionization stages of C, N, O, Ne, Mg, Si, Ar, Ca, Fe and Ni in the form q1c (Te ) = A1c T e exp(- ) I 30 cm3 /s, (3.1)


where as in the previous chapter = I/kTe = Tc /Te ; I = kTc is the ionization energy from the ground state. For most cases a 0.1. The last value holds always if kTe > 1 eV. The values of A1c and Tc are given in Table 5. The formula for the collisional ionization rates for atoms and ions of isoelectronic series from H to Ni have b een generalized in the pap er by Arnaud & Rothenflug (1985) and they gives the form q1c (Te ) = 6.69 · 10- (kTe )3/2
7

F (j )
j

exp(-j ) cm3 /s, j

(3.2)

where j = Ij /kTe and Ij is the ionization energy from level j and F (j ) = Aj {1 - j · f1 (j )} + Bj {1+ j - j (2 + j ) · f1 (j )}+ +Cj · f1 (j )+ Dj · j · f2 (j ), f1 ( ) = e E1 ( ) , f2 ( ) = e
1

(3.3)

e-t ln tdt. t

The numerical values of Ij , Aj , Bj , Cj and Dj are given in Table 10. Integral exp onential function E1 ( ) can b e calculated by the usual manner (see, for example, Abramowitz & Stegun (1964)). The function f2 ( ) can b e expressed with error ab out 1% in the following form (Hummer (1983)): f2 ( ) = P ( )/(Q( ) 2 ) , where
13

(3.4)

P ( ) =
j =0



-j

14

pj ,

Q( ) =
j =0



-j

q

j

The values of parameters pj and qj in series expansion of f2 ( ) given in ab ove cited pap er. Shevelko et al. (1983) using the cross sections of collisional ionization calculated in the Coulomb-Born approximation found more simple analytical expression for the collisional ionization rate q1c (Te ) for the outermost shell (nl)q , namely 10-8 q · [IH /I ]3/2 exp (- ) · q1c (Te ) = + 31 A , (3.5)


where as former, = I/kTe and I is the ionization energy (from the ground level) and the quantities A and are the parameters, the values of which for some atomic shells are presented in Table 11. The error estimation of this approximation for collision ionization rate is ab out 6% for 0.1< <10. Eq.(3.5) is applicable for all elements, but at small values of Z the error increases. The rate of collisional ionization (in units cm3 s using the formula by Burgess & Chidichimo (1983) q1c (Te ) = 2.17 · 10-8 C
j - = [ln(I/Ij + j 1 )]/((I +kTe )/Ij ) -1

) for complex ions can also b e calculated

qj (IH /Ij )3/2 · j E1 (j ) · , , (3.6) (3.7)

1/2

= (1/4) ·{[(100 Z + 91)/(4 Z +3)]1/2 - 5}.

In expression Eq.(3.6) qj is the numb er of electrons in shell j and Ij is the corresp onding ionization energy. Summation over all shells of the atomic configuration takes into account also the electron excitation from internal shells and the processes of autoionization. The values of parameters C, Ij and qj are given in Table 12. If the contribution of autoionization is negligible then the letter "a" has b een added to the ion symb ol and if it is essential then the letter "b". Symb ol (i) added to qj values denotes presence of strong resonances in ionization cross sections for corresp onding shells, but symb ol (ii) denotes presence of large numb er of weak resonances. For light ions with 2 Z 5 we can take C =2.30 (± 19%). This value is well consistent with the value 2.2 found by Seaton (1964). If we incorp orate approximately the contributions of autoionization then C =2.70, which is close to the value 2.77 found by Lotz (1968). Comparison of the collision ionization rates given by Arnaud & Rothenflug (1985) with corresp onding data by other authors showed that the discrepancy with the data by Summers (1974) and by Burgess

32


& Chidichimo can reach from 1.2 to 2 times, but the consistency with reformulated results by Lotz (1967, 1968) is good. References to the many modern collision ionization data for astrophysically imp ortant ions are given by Butler (1993), see also App endix A. 3.2 The electron impact excitation Excitation of atoms by electron impacts is the main mechanism of the formation the sp ectral lines b etween low excited levels in the sp ectra of gaseous nebulae. The electron impact excitation rates usually are expressed via the effective collision strengths ij : qij = 8.6287 · 10- gi Te
1/2 6

ij exp(-ij ) .

(3.8)

Here gi is the statistical weight of the lower state i. The coefficient of collisional deactivation can b e written in the form qji = 8.6287 · 10-
1/2 gi Te 6

ij ,

(3.9)

and it is interrelated to the coefficient of collisional excitation by the relation gj exp(-ij ) , gi

qij =

(3.10)

The quantity ij is determined by integrating the collision strength ij over the Maxwell electron velocity distribution :


ij =


o

ij

exp(-ij u) d(ij u) .

(3.11)

In the formulae (3.8 - 3.11) ij = Eij /kTe and u = E/Eij - 1 is the energy E of removed electron in the ionization threshold units. Using the exp erimental and theoretical excitation cross sections for transitions b etween hydrogen states Giovanardi et al. (1987) have determined the effective collision strengths ij (Te ) 33


for 15 lower states. For 4 lowest levels the transitions b etween sublevels with different orbital quantum numb ers have b een considered. The effective collision strengths were approximated by expression
2 3 ij = a + bTe + cTe + dTe ,

(3.12)

The values of p olynomial fit parameters a, b, c and d are given in Table 13. The effective collision strengths for HeI I have b een found by Hummer and Storey (1987). These can b e well presented by the same p olynomial fit for temp eratures up to 105 K. The values of corresp onding coefficients are also given in Table 13. The values of qij computed for HI by using the expressions (3.8) and (3.10) and data of Table 13 at different values of Te are given in Table 14, where are also given the total coefficients of electron impact excitation summed over all levels j 15. This quantity is useful for calculating the ionization state of HI atoms in the nebulae. The coefficients of collisional excitation of complex ions have b een given by Clark et al. (1982). The collisional strengths for different atoms and ions of isoelectronic sequences of H, He, Li, Be, B, Na, Mg have b een presented by expression (Z, X ) = [Z + b1 + d1 /Z ]-2 [c0 + c1 /X + c2 /X 2 ]+ [Z + b2 + d2 /Z ]-2 (c3 ln(X )+ c4 ), (3.13)

where X = E/Eij = u + 1, Z is the nuclear charge numb er and the values of parameters b1 , b2 , c0 , c1 , c2 , c3 , d1 and d2 are given in Table 15. Integrating over the Maxwellian velocity distribution of electrons the corresp onding coefficient of collisional excitation can b e written in the form qij (Te ) = F1 (Z )CE [ + F2 (Z )CE [ c0 exp(- ) + c1 E1 ( )+ c2 E2 ( )]+ c3 E1 ( ) c4 exp(- ) + ] cm3 /s, (3.14)

34


where = Et /kTe , CE = 8.010 · 10-8 /[(2L + 1)(2S + 1)Te

1/2

], F1 (Z ) = [Z + b1 + d1 /Z ]-2 ,

F2 (Z ) = [Z + b2 + d2 /Z ]-2 and En ( ) is the integro-exp onential function of n th order:


En ( ) =

1

e-t dt . tn

For different atoms and ions of the ab ove mentioned sequences the energy Eij has b een expressed in the form Eij = a0 + a1 Z + a2 Z 2 + a3 Z 3 + a4 Z 4 , Values of the parameters a0 , a1 , a2 , a3 and a4 are also given in Table 15. The values of the transition probabilities and ij for the large numb er of forbidden and intercombination lines which are observed in the sp ectra of planetary nebula are given in Table 17. An explication of used designations for the levels and their energies is given in Table 16. Due to limited space of the catalogue we present data only for ions od Be, B, O and Mg sequence which are taken from Mendoza (1983). The modern data can b e found in the original pap ers cited in App endix A. (3.15)

35


3.3 Excitation by collision with heavy particles Process of the atom and ion excitation by heavy particle collisions differs essentially from that by electon impacts. Large mass particles move much slower than electrons and pass nearby the excited atom during a long time interval. If the energy of the transition E in the target atom or ion is comparable with the kinetical energy E of the colliding particle then the excitation cross sections are very small due to the fast oscillation of the target wave function with the phase Et/h. On the contrary, in the case if E E this phase is small and the total excitation cross section by a heavy particle is not small and can exceed the appropriate cross section for excitation by electron impacts. This means that the heavy particle collisions are the effective ones for the excitation of the fine structure transitions or for the orbital moment redistribution due to transitions b etween the high-excited Rydb erg states. Proton collisions are most effective for generating transitions if E E . For such transitions the excitation rates of neutral targets by proton impacts are (Mp /me )1/2 times larger than those by electron impacts (Seaton (1955); see, also, Dalgarno (1984)). The proton collisions are effective for the fine structure levels excitation and for excitation of the transitions b etween sublevels nl: p + H (nl) p + H (nl ) . Cross sections for this process have b een calculated by Pengelly and Seaton (1964) in the framework of the semiclassical p ertubation theory. At large values of n the proton collisions lead to the statistical equilibrium distribution of atoms on nl sublevels. For large values of n and n the proton impact excitations p + H (n) p + H (n ) . are also effective (Burgess & Summer (1976)). In excitation of the p ositive ions by proton impacts the Coulomb interaction must b e taken into account. This interaction diminishes the proton-impact excitation rates and in turn increases the excitation rates by electron impacts. The role of this effect is negligible if n 1 at 4K . typical in astrophysical ob jects values Te 10 Proton collisions are very effective for excitation of the fine structure levels of CI, OI, OI I and of many other ions. Numerous references in the field are presented in App endix A. At low temp eratures (T 103 K ) the exitation by proton collisions can more than ten times exceed the excitation bye electron impacts (Rouef and Le Bourlot (1990), see Table 18 and also Fig. 3.1). Excitation by collision with HI are effective for the fine structure levels. Collisions with more heavy particles are less effective than neutral hydrogen excitation due to their less abundances. The references in the field can b e found in App endix A.

36


3.4 Autoionization The autoionization process comprises of collisional excitation of an atom or ion to autoionization states followed by autoionization decay. Similarly to the photoionization processes, autoionization by electron impacts generates the resonances in the cross sections. Autoionization is usually essential at Te 105 K for atoms and ions having more than two electrons. The numb er of autoionization acts p er unit volume and unit time is N = n(X i ) ne · q (Te ) , (3.16)

where qa (Te ) is the autoionization rate. The most complete compilation of analytical expressions and corresp onding data for determination of qa is given in pap er by Arnaud & Rothenflug (1985) the results of which we reproduce here. 1. The formula for lithium isoelectronic series is q (Te ) = 1.92 · 10-
7

b exp(- )G( ) cm3 /s , 2 (kT )1/2 Zef e

(3.17)

where = I /kTe , G( ) = 2.22 f1 ( )+0.67[1 - f1 ( )] + 0.49f1 ( )+1.2 [1 - f1 ( )] , b = [1 + 2 · 10-4 Z 3 ]-1 , Zef = (Z - 0.43) , I = 13.6{(Z - 0.835)2 - 0.25(Z - 1.62)2 } eV , and function fi ( ) is given by Eq.(3.3). Formula (3.17) corresp onds to the 1s - 2p transition corrected for the contribution of other transitions by multiplying with coefficient 1.2. Comparison of the qa values, given by Eq.(3.17) with existing measurements showed that the results can differ from them not more than ab out two times. 2. For ions of sodium isoelectronic series q (Te ) = 6.69 · 10-
7

· I exp (- ) {1+( )} cm3 /s . (kTe )1/2

(3.18)

If 12 Z 16 then ( ) = -f1 ( ), I = 26(Z - 10) eV and = 2.28 · 10-17 (Z - 11)-0.7 cm2 If 18 Z 28 then ( ) = -0.5[ - 2 + 3 f1 ( )] ,

(3.19)

and I = 11(Z - 10)3/2 eV, = 1.310-14 (Z - 10)-3.73 cm2 . 3. For the ions of isoelectronic series set from the magnesium series to the sulphur series (Z < 16) the expression for ( ) is given by Eq.(3.19) where = 4.0 · 10-13 Z -2 cm2 and I = 10.3(Z - 10)-1.52 eV for the Mg isoelectronic sequence, I = 18.0(Z - 11)-1.33 eV for the Al isoelectronic sequence, I = 18.4(Z - 12)-1.36 eV for the Si isoelectronic sequence, I = 23.7(Z - 13)-1.29 eV for the P isoelectronic sequence, I = 40.1(Z - 14)-1.10 eV for the S isoelectronic sequence.

37


For ions of other series the contribution of autoionization to the total collision excitation rate can b e ignored. 3.5 Dielectronic recombination The process of dielectronic recombination, describ ed by scheme (2.7), proceeds in two stages. At the first stage the electron is captured in an autoionization state b elonging to ion Xi+1 . At the second stage there proceeds the radiative decay of the state with generation of a b ound state of ion Xi . At high temp eratures Te 105 - 106 K the main contribution into the dielectronic recombination rate is given by the recombination processes to the autoionization states with large principal quantum numb ers n. These states decay easily in electron collisions and due to external radiation field. Thus, the dielectronic recombination rate dep ends heavily on the physical conditions in plasma. At high electron densities ne > 1013 - 1015 cm3 b oth the collisional ionization from autoionization states and collisional p opulation of them are essential. The photons irradiated in the processes of dielectronic recombination due to transitions b etween autoionization states are named as the dielectronic satellites. The numb er of dielectronic recombination acts for ion Xi+1 p er unit volume and unit time is N
di

= n(Xi+1 ) ne di (Xi+1 ) ,

cm3 /s ,

(3.20)

where di (Te ) is the dielectronic recombination rate. The semiempirical formulae for dielectronic recombination rates have b een given by Burgess (1965), Landini & Monsignori (1971), Jain & Narain (1976). The revised expression for di (Te ) with the modified values of excitation cross-sections of ions Xi+1 due to electron collisions has b een given by Alam & Ansari (1985). The differences of di (Te ) values found by various authors for many ion sp ecies reaches 1dec. This is caused by the difficulties in computing the reliable values of excitation cross-sections, the main factor among these b eing the necessity to take into account transitions from all autoionization states and cascade transitions from these states. Usually the dielectronic recombination rate is computed in the Burgess (1965) approximation. This approximation holds for most ions at high electron temp eratures Te > 105 K. A simple approximation formula for di (Te ) has b een given in pap ers by Aldrovandi & Pequignot (1973, 1976) who modified the Burgess approximation to the form
- di = Adi Te H 3/2

exp (-T0 /Te )[1 + Bdi exp (-T1 /Te )].

(3.21)

Here the index H marks the Burgess (High temp erature) approximation. The same expression has b een prop osed also by Shull & Van Steenb erg (1982), who also used the semiempirical formula by Burgess (1965) and improved the numerical values of approximation parameters Adi , Bdi , T0 and T1 for all ions of chemical elements from C to Ni which are given in Table 5. The same expression holds also for He+ . Arnaud & Rothenflug (1985) started from the expression of di given in the pap er by AlH drovandi & Pequignot (1973) and corrected by a factor prop osed by Burgess & Tworkowski 38


(1976). For Li - like ions they obtained the following formula: di = 7.6 · 10- H where = I0 /kTe , z = Z - 2. A(z ) = (z +1)3 /z 2 (z 2 +13.4)1/2 [1 + 0.16(z +1)+0.017(z +1)2 ], (z +1)2 /[1 + 0.015z 3 /(z +1)2 ]. z2 In these formulae I0 is the ionization p otential for the ion studied and Z is its nuclear charge. The values of coefficients di (Te ) computed using Eq.(3.22) are smaller than the corresp onding values found by Shull & Van Steenb erg (1982), b eing multiplied by coefficients 0.19, 0.44, 0.36 and 0.41 for ions of O, Mg, Ca and Fe, resp ectively. For high-charge ions we can use the di (Te ) values from pap er by Shull & Van Steenb erg (1982), multiplying the values by 0.30 for ions of Ne and by 0.40 for ions of Si, S and Ar. The values of di (Te ) also based on the Burgess approximation for all ions of C ­ Ni and for some other isoelectronic sequences have b een given in pap ers by Jacobs et al. (1977a, 1977b, 1980), where the autoionization processes have also b een incorp orated. The results of the last pap ers have b een improved by Woods et al. (1981), Shull & Van Steenb erg (1982). A simple approximation formula for the total dielectronic recombination rate has b een given by Romanik (1988) for ions of He, Li, Be and Ne sequences: D(z ) = 3.0
- di = Te H 3/2 i 11

A(z ) exp [-D(z ) ]

3/2

,

cm3 /s ,

(3.22)

ai exp (-Ti /Te ) cm3 /s .

(3.23)

In this expression all imp ortant radiative and autoionization processes have b een taken into account. The numerical values of parameters Ti and ai are given in Table 19. At large electron temp erature the high excited levels are p opulated predominantly by the dielectronic recombination which proceeds via electron capture into these states. For most elements at 105 ­106 K the dielectronic recombination dominates over the radiative recombination. At temp eratures Te 104 K the efficiency of captures into high excited states is low. For ions of C, N, O, Ne, Al and Si the dielectronic recombination can proceed via captures into lower autoionization states. Due to presence of such states the process of dielectronic recombination is essential also at low temp eratures Te = 5 000 ­ 20 000K which are dominant in nebulae. The capture processes to lower autoionization states determine the rate of low-temp erature dielectronic recombination. Some of the ions of the ab ove-mentioned elements have low metastable states. The numb er of autoionization captures and thus the dielectronic recombination rate in these cases dep end on the p opulation of corresp onding metastable states and, consequently, on the electron concentration and temp erature of nebula. The dielectronic recombination at low temp eratures acts on the intensities of some emission lines observed in the sp ectra of nebulae.

39


The dielectronic recombination rate at low temp eratures (applied to the conditions of gaseous nebulae) has b een calculated by Storey (1981), Nussbaumer & Storey (1983, 1984, 1986, 1987). Corresp onding coefficient di (Te ) has b een expressed by the following approximation L a di (Te ) = ( + b + ct + dt2 ) t L t
-3/2

exp (-f/t)10-

12

cm3 /s .

(3.24)

This expression describ es the dielectronic recombination on the ground or the metastable state. In Table 20 are presented the values of parameters a, b, c, d and f and values tl and Y for ions of C, N, O, Ne, Mg, Al and Si taken from the pap ers by Nussbaumer & Storey (1984, 1986, 1987). In the table the quantity E is the calculated excitation energy of the term, the value of tl has b een chosen such that the maximum error in the fit formula Eq.(3.24) were less than 20 % . The value Y is the rate di at Te = 104 K in units of 10-12 [cm3 s-1 ]. For ions of Mg, Al, Si and Ne also the values of total dielectronic recombination rates di (total) = di (LS ) have ef b een given in Table 20. In this formula the summation is carried out over b oth ground and metastable states. More exact calculations of the dielectronic recombination rates for ions CI I, NI I I and OIV have b een carried out in the pap er by Badnell (1988). These quantities do not differ from the results by Nussbaumer & Storey (1984, 1986, 1987) more than 10­20%. Necessity to take into account the forbidden autoionization transitions in the calculation of dielectronic recombination rate has b een demonstrated by Beigman & Chichkov (1980). The total recombination rate can b e written in the form = rad (Te )+ di (Te )+ di (Te ). H L (3.25)

If Te 103 K then this rate is dominantly the radiative recombination arad (Te ) and at Te > 105 K dominates the dielectronic recombination via the captures to high excited autoionization states di (Te ), see Eq.(3.21). For intermediary temp eratures Te =103 ­ 104 K for many ion sp ecies H the dominating process is the dielectronic recombination via low excited autoionization states (di (Te )). The contribution of individual recombination transitions to the total recombination L rate is visualized in Fig.10 of the monograph by Nikitin et al. (1988). 3.6 The charge transfer reactions In charge transfer reactions an electron (usually the outermost one) is transp orted from atom or ion X to ion X+ : (3.26) X+ +Y X+ Y+ ± E. The electron transition is realized via quasimolecular state X+ Y or XY+ . The energy defect E equals to the difference of binding energies of atomic systems X+ Y and XY + . In the case of direct reaction an electron of atom Y is transferred to ion X+ . Such charge transfer is ionization of Y and recombination to X+ . The opp osite charge transfer is called the inverse charge transfer. The rates of direct and inverse reactions are not equal and the ratio dep ends on the gas temp erature.

40


For energies of colliding particles E 100 eV the most imp ortant process is the capture by the outermost shell. At large energies of colliding particles more effective processes of electron capture by internal shells. For atoms of alkali metals the electron by internal shells is essential already at E >20 eV. The reactions of typ e X+ +X0 X0 +X+

electron are the capture

(3.27)

are named the reactions of resonance charge transfer, the role of such processes is minor for gaseous nebulae. Dominating in the conditions of gaseous nebulae are the reactions of charge transfer in collision with neutral hydrogen and helium: Xi+1 +H0 Xi +H+ and Xi+1 +He0 Xi +He+ . (3.29) (3.28)

However, in some cases also other reactions of typ e (3.26) for element different from H and He can b e imp ortant. The numb er of direct (or recombination) charge transfer acts (Eq.(3.28) and Eq.(3.29)) in the unit volume p er unit time is N ch = n(Xi+1 ) n(Y0 ) k (Xi , Y0 ) (3.30)

and the same numb er for inverse (or ionization) charge transfer (see also Eqs.(3.28-3.29)) is Nch = n(Xi ) n(Y+ ) k (Xi , Y+ ), (3.31)

where Y0 corresp onds to H0 or He0 and Y+ to H+ or He+ . The quantites k and k are the corresp onding charge transfer rates (cm3 /s). The values k and k for different ions, the lines of which are observed in the nebulae, are summarized by Table 21. Before the charge transfer reaction the ion Xi+1 is predominantly in the ground state, but in the result of the charge transfer reaction the excited states of ion Xi can b e p opulated. The quantities k and k are interrelated by the following formula of statistical thermodynamics: (3.32) k = k · exp(-E/kTe ). The main direct and inverse charge transfer reactions of the typ es Eq.(3.28) and Eq.(3.29) are essential in the low-density astrophysical plasma conditions have b een considered by Arnaud & Rothenflug (1985). They found the following approximation formula for computation of the charge transfer rates: k = A · (Te /104 )B · 1+ C exp [D(Te /104 )] cm3 /s. (3.33)

41


In this expression the dep endence of corresp onding coefficients on Te has b een describ ed analytically. The values of parameters A, B , C and D are given in Table 22, where in the column 2 the range of Te values has b een given for which approximation formula (3.33) holds. Some valuable data ab out charge transfer reactions are given by Suchkov & Shchekinov (1983). They used for reactions with H0 and He0 the approximation C =0, i.e. in their formulation k = k0 Te The values of coefficients k0 and are compiled in Table 23. The data for charge transfer rates in impacts b etween atoms and ions of heavy elements are given by Pequignot & Aldrovandi (1986). The values of k for each pair of ions (upp er value) and the values of E (lower value) are given in Table 24. The charge transfer reaction b etween the heavy elements can b e essential in the interstellar medium, in HI regions of nebulae and in the atmospheres of cool stars. In the conditions of low-density astrophysical plasma, esp ecially in gaseous nebulae, the charge transfer reactions (e.g., O+ +H0 O0 +H+ ) often determine the atom ionization state. H+ / H0 This fact was first demonstrated by Chamb erlain (1956), who found that O+ / O0 in the most of the gaseous nebulae. This relation holds due to high rates of the corresp onding charge transfer reaction. The rates of this reaction have b een computed by Field & Steigman (1971). Steigman et al. (1971) have given the rates of reaction N+ +H0 N0 +H+ . More exact values of charge transfer rates have b een found by Fehsenfeld & Ferguson (1972) for reaction O+ +H0 O0 +H+ +0.22 eV, and by Butler & Dalgarno (1979) for reaction N+ +H0 N0 +H+ + 0.95 eV (see Table 21). Tarter et al. (1979) studied the effect of double charge transfer on the ionization state of gas medium: Xi+2 +He0 Xi +He++ , finding these to b e negligible. Unfortunately, the exactness of numerical values of charge transfer rates k for many reactions is low and the results by different authors can differ to dex due to low quality of methods of computation of charge transfer rates. Unknown are the reaction rate dep endence on Te for many reactions and the values of k for multiply ionized atoms. Probably the low precision of charge transfer rates is one of factors for giving inexact results for calculated ionization degree of elements in the gaseous nebulae.

42